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**Some Developments in the Theory of Shape Constrained Inference.** / Groeneboom, Piet; Jongbloed, Geurt.

Research output: Contribution to journal › Article › Scientific › peer-review

Groeneboom, P & Jongbloed, G 2018, 'Some Developments in the Theory of Shape Constrained Inference' *Statistical Science*, vol. 33, no. 4, pp. 473-492. https://doi.org/10.1214/18-STS657

Groeneboom, P., & Jongbloed, G. (2018). Some Developments in the Theory of Shape Constrained Inference. *Statistical Science*, *33*(4), 473-492. https://doi.org/10.1214/18-STS657

Groeneboom P, Jongbloed G. Some Developments in the Theory of Shape Constrained Inference. Statistical Science. 2018;33(4):473-492. https://doi.org/10.1214/18-STS657

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title = "Some Developments in the Theory of Shape Constrained Inference",

abstract = "Shape constraints enter in many statistical models. Sometimesthese constraints emerge naturally from the origin of the data. In other situations,they are used to replace parametric models by more versatile modelsretaining qualitative shape properties of the parametric model. In this paper,we sketch a part of the history of shape constrained statistical inference in anutshell, using landmark results obtained in this area. For this, we mainly usethe prototypical problems of estimating a decreasing probability density on [0,∞) and the estimation of a distribution function based on current statusdata as illustrations.",

author = "Piet Groeneboom and Geurt Jongbloed",

year = "2018",

doi = "10.1214/18-STS657",

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journal = "Statistical Science",

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AU - Jongbloed, Geurt

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N2 - Shape constraints enter in many statistical models. Sometimesthese constraints emerge naturally from the origin of the data. In other situations,they are used to replace parametric models by more versatile modelsretaining qualitative shape properties of the parametric model. In this paper,we sketch a part of the history of shape constrained statistical inference in anutshell, using landmark results obtained in this area. For this, we mainly usethe prototypical problems of estimating a decreasing probability density on [0,∞) and the estimation of a distribution function based on current statusdata as illustrations.

AB - Shape constraints enter in many statistical models. Sometimesthese constraints emerge naturally from the origin of the data. In other situations,they are used to replace parametric models by more versatile modelsretaining qualitative shape properties of the parametric model. In this paper,we sketch a part of the history of shape constrained statistical inference in anutshell, using landmark results obtained in this area. For this, we mainly usethe prototypical problems of estimating a decreasing probability density on [0,∞) and the estimation of a distribution function based on current statusdata as illustrations.

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